Whats the pertinent laws regarding contact lenses on shabbos and yom tov, i.e. keeping them moist after use and cleaning them, etc? All pertinent laws? Are there different opinions?
There are two principle issues concerning contact lenses on Shabbos.
One — the main issue — is the question of cleaning soft contact lenses. Some poskim are stringent concerning using the regular saline solution (see Kovetz Teshuvos no. 26), and others — including Rav Shlomo Zalman Auerbach (see Shmiras Shabbos Ke-Hilchasah p 181, and Nishmas Avraham 5, p. 20), are lenient. There is room to be lenient, based on this ruling.
For a more detailed article on this subject, please see here.
A second issues is wearing contact lenses in the public domain. Once a person has become accustomed to them, there is no problem in this, because there is no concern that they will be taken out of the eye and carried in the public domain. However, before a person has grown accustomed to contact lenses, he often has to remove them to arrange them properly in the eye. Therefore, one should not wear contact lenses in a public domain on Shabbos until he has grown accustomed to them and wears them comfortably.